19frac{2sqrt{3}}{2sqrt{3}-3sqrt{2}} eching

$$19 \frac { 2 \sqrt { 3 } } { 2 \sqrt { 3 } - 3 \sqrt { 2 } }$$

Baholash

$$-19\sqrt{6}-38\approx -84,540305113$$

Yechim qadamlari

\frac{2\sqrt{3}}{2\sqrt{3}-3\sqrt{2}} maxrajini 2\sqrt{3}+3\sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{\left(2\sqrt{3}-3\sqrt{2}\right)\left(2\sqrt{3}+3\sqrt{2}\right)}$$

Hisoblang: \left(2\sqrt{3}-3\sqrt{2}\right)\left(2\sqrt{3}+3\sqrt{2}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{\left(2\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}$$

\left(2\sqrt{3}\right)^{2} ni kengaytirish.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{2^{2}\left(\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{4\left(\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{4\times 3-\left(-3\sqrt{2}\right)^{2}}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-\left(-3\sqrt{2}\right)^{2}}$$

\left(-3\sqrt{2}\right)^{2} ni kengaytirish.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-\left(-3\right)^{2}\left(\sqrt{2}\right)^{2}}$$

2 daraja ko‘rsatkichini -3 ga hisoblang va 9 ni qiymatni oling.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-9\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-9\times 2}$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{12-18}$$

-6 olish uchun 12 dan 18 ni ayirish.

$$19\times \frac{2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)}{-6}$$

-\frac{1}{3}\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right) ni olish uchun 2\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right) ni -6 ga bo‘ling.

$$19\left(-\frac{1}{3}\right)\sqrt{3}\left(2\sqrt{3}+3\sqrt{2}\right)$$

-\frac{1}{3}\sqrt{3} ga 2\sqrt{3}+3\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$19\left(-\frac{1}{3}\sqrt{3}\times 2\sqrt{3}-\frac{1}{3}\sqrt{3}\times 3\sqrt{2}\right)$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$19\left(-\frac{1}{3}\times 3\times 2-\frac{1}{3}\sqrt{3}\times 3\sqrt{2}\right)$$

3 va 3 ni qisqartiring.

$$19\left(-2-\frac{1}{3}\sqrt{3}\times 3\sqrt{2}\right)$$

3 va 3 ni qisqartiring.

$$19\left(-2-\sqrt{3}\sqrt{2}\right)$$

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$19\left(-2-\sqrt{6}\right)$$

19 ga -2-\sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-38-19\sqrt{6}$$